1. Quantum Computing
BCS Belgium Branch

2. Quantum Computing Basic Quantum Mechanics Quantum Algorithms
Quantum Computer Hardware

3. Basic Quantum Mechanics
Wave particle duality
Coherence
Interference
Young’s slits
Entanglement
Observer matters
Classical physics
Exact knowledge
Deterministic

4. Beam Splitter
Split light beam with semi silvered mirror A B

5. Interference
Split and recombine light beams A B

6. Interference
Split and recombine light beams A B

7. Young’s slits
Diffraction patterns

8. Wave Interference + + = =

9. EPR Paradox Quantum Teleportation made real
Teleportation diagrams Courtesy of IBM, Copyright, IBM Corp, 1995

10. Quantum Interference Superpositions of quantum states
Wavefunctions are complex
Modulus has a physical interpretation

11. Classical Bits are 0 or 1 1 Classical CPUs use binary representation
Only 0 or 1 is defined
N-bit register contains one number from 2N

12. Qubits are the key |1> |0> -|0> -|1>
Quantum CPU works on Qubits
Represent 0 and 1
Or any mixture
N-bit register may contain any subset of numbers from 2N
-|0>
|0>
-|1>

13. Hadamard Transform 1 1 -1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 -1 -1 1
Controlled mixing
Given a system with eigenstates |0> |1>
Forms
|0> + |1>
|0> - |1>
Self inverse 1
1 -1

14. Quantum registers |0> + |1> is 0 and 1 Entangle 3 qubits
And you get
|000> + |001> + |010> +|011> + |100> + |101> + |110> + |111>
L operations
2L different numbers
|0>+|1>
|0>+|1>
|0>+|1>
|0>+|1>
|0>+|1>
|0>+|1>

15. Deutsch ’85 Problem H Uf H |0> answer |0> - |1>
Given f(x) , x = {0,1}
Compute once
Decide if f(0)=f(1)
Impossible for classical CPU

16. Conditional Test Classical Quantum if (x) if (qb) False True -|0>
|1>
-|1>
|0>

17. Simon’s Algorithm ‘93 Given a periodic function of period r
f(x)=f(x+r)
Find period r in polynomial time
Single step finds all possible values of r
Bad news r, 2r, 3r,… Nr all solutions too!
Good news GCD is easy on classical CPU

18. Factoring Composites Factoring is slow for conventional CPUs
Simple example – factorise
35 = ? x ?
221 = ? ? x ? ?
29083 = ? ? ? x ? ? ?
Multiplying is much easier
123 x 456 = ? ? ? ? ?

19. Factoring Composites 2 Factoring is slow for conventional CPUs
Simple example – factorise
35 = 5 x 7
221 = 13 x 17
29083 = 127 x 229
Multiplying is much easier
123 x 456 = 56088

20. Periodicity Factorisation
a < N chosen at random
Prob( GCD(a, N) = 1 ) > 1 / log N
GCD (a, N) = 1
f(x) = a x mod N
Find period r using quantum machine
Factors are GCD ( a r/2 mod N + 1, N )
Fast periodicity determination => Factors

21. Shamir’s Twinkle Hardware accelerator for classical CPUs
Optoelectronic device ~1000x faster
512bit RSA keys vulnerable
Past dedicated hardware triumphs include
WWII Colossus just beats a Pentium
Turing’s Bombe still 60x better

22. Grover’s Algorithm ‘96 H Alice |0> := -|0> Bob |k> := -|k>
Find a match in N unsorted records
Classical brute force time ~ N/2
Quantum algorithm time ~ N1/2

23. Searching Grovers algorithm using Q comparisons
N1/2 = 1 / sin ( p / 2(2Q+1))
N ~ 4 (2Q+1)2 / p2
Q N 4 10 20 33

24. Is Life a Quantum Computer?
Q=1, N=4 DNA uses a 4 base code
UCAG
Q=3, N=20 Life uses ~20 amino acids
Genetic code has supersymmetry
Weird coincidence or deep link to QM ??
Decoherence time seems too short

25. DNA Code of Life

26. DNA Computing Adleman - Travelling salesman problem
Fast combinatorial solutions
Hard to set up
Answer fast
Interpretation slow

27. DNA Turing Machine Universal computing machine Molecular computing
DNA is program tape
Enzymes are hardware
Nature 22 Nov 2001

28. Quantum Computer Hardware
Toy versions exist, algorithms work
2 qubit Chloroform CHCl3
3 qubit Trichlorethylene CHCl=CCl2
Other possibilities
Josephson Junctions
Ion traps, BECs

29. Chloroform 2 Qubits Nuclear spin resonance 1H – hydrogen 13C – carbon
Complex chemical analysis
Simple molecules
Program by RF pulses

30. Programming Hardware dependent RF pulses Tuned lasers Read back output
NMR spectrum
NMR Animation, Courtesy of IBM, Copyright, IBM Corp, 1995

31. The Race for More Qubits
Date
Group
Compound
Qubits
1998
IBM
Chloroform 2
IBM/MIT
Trichloroethylene 3
Mar 2000
LANL
Crotonic acid 7
Aug 2000
MIT
Fluorine 5

32. References
There is a lot of information available on the web from the various research groups that have specialised in quantum algorithm development and design of hardware for quantum computers.
  I created this talk from a number of sources, but the ones below and their links contain additional material at a range of different levels from the basics up to and including the latest work.

33. Weblinks General reviews at many levels
Scientific American review article   
Physics and computer science
University level algorithms

34. Weblinks Practical Hardware Developments
Quantum Experimental Kit
NMR Quantum Computers
LANL 7 Qubit Machine
Quantum Teleportation

35. Weblinks Other Related Articles EU Quantum Projects
 Other Related Articles
EU Quantum Projects
Shamir’s Twinkle
DNA Computing
DNA Turing Machine
Speculative